3 Attachment(s)

How do I manipulate small finite increments? How do I know what assumption is valid?

Hello,

I know certain things about small finite increments, like how the general formula for dy/dx is derived, but I have no idea how to manipulate the infinitesimals. The assumptions made seems arbitrary to me, how do I know that it is ok to assume one thing, but wrong to assume in case of others? I mean I can understand that this follows from that assumption and etc, but what made the assumptions valid I have no idea. Can you please explain to me the concept of delta x, or give me links to some resources so that I can understand at least well enough to get sums like these done from scratch: (Nod) (Nod)

http://www.mathhelpforum.com/math-he...1&d=1274494115

http://www.mathhelpforum.com/math-he...1&d=1274494214

http://www.mathhelpforum.com/math-he...1&d=1274494246